A new ternary compound with the BGa8Ir4 structure type in the Al–Au–Ir system

Kadok, J.; de Weerd, M.-C.; Boulet, P.; Fournée, V.; Ledieu, J.

doi:10.1107/S2052520618016712

research papers

STRUCTURAL SCIENCE
CRYSTAL ENGINEERING
MATERIALS

ISSN: 2052-5206

Volume 75| Part 1| February 2019| Pages 49-52

https://doi.org/10.1107/S2052520618016712

A new ternary compound with the BGa₈Ir₄ structure type in the Al–Au–Ir system

Joris Kadok,^a Marie-Cécile de Weerd,^a Pascal Boulet,^a Vincent Fournée ^a and Julian Ledieu ^a ^*

^aInstitut Jean Lamour (UMR7198 CNRS, Université de Lorraine), Campus ARTEM 2 allée André Guinier, 54011 Nancy Cedex, France
^*Correspondence e-mail: julian.ledieu@univ-lorraine.fr

Edited by M. de Boissieu, SIMaP, France (Received 15 October 2018; accepted 23 November 2018; online 23 January 2019)

Following the recent determination of the Al₃AuIr structure, a new ternary phase has been identified in the Al–Au–Ir phase diagram. It has a chemical composition Al₉(Au;Ir)₄ with an apparently low gold content. Its crystal structure has been determined with single-crystal X-ray diffraction. The new compound crystallizes in the tetragonal crystal system and has been successfully solved in space group I4₁/acd (Pearson symbol tI104) with lattice parameters a = 8.6339 (2) and c = 21.8874 (7) Å. Atomic environments are described as well as similarities with the BGa₈Ir₄ compound.

Keywords: intermetallic; X-ray diffraction; crystal structure; entropy.

CCDC reference: 1881225

1. Introduction

The Al–Ir system has several intermetallic compounds in the Al-rich part of the phase diagram: Al₉Ir₂, Al₄₅Ir₁₃, Al₂₈Ir₉, Al_2.75Ir and AlIr (Okamoto, 2009 ). The crystal structures of the compounds in this system can be of great complexity. Indeed, the Al₄₅Ir₁₃ and Al₂₈Ir₉ compounds crystallize in their own structure type, both containing 236 atoms in their respective unit cell. The Al–Au system also includes several intermetallic compounds across the whole range of the phase diagram: Al₂Au, AlAu, AlAu₂, Al₃Au₈ and AlAu₄ (Okamoto, 1991 ). The crystal structures of these compounds are simpler than those from the Al–Ir system with the exception of the Al₃Au₈ phase which has 132 atoms in the unit cell (In₃Yb₈ structure type).

Unlike the two Al–Ir and Al–Au systems, Au and Ir are not miscible and do not form any intermetallic compound. According to Dubois & Belin-Ferré (2011 ), structurally complex metallic alloys (CMAs) are likely to be found in ternary systems like Al–Au–Ir in which two transition elements are immiscible. CMAs are of great interest as they exhibit unique properties that differ from those of their main constituents or structurally simpler compounds. Recently, investigation of the Al–Au–Ir system has revealed the existence of the Al₃AuIr compound (Kadok et al., 2015 ). This compound is of the Ni₂Al₃ structure type and exhibits a split Al atomic position originating from the mixed occupancy of another Au/Ir atomic position. Ab initio calculations suggested a Hume–Rothery stabilization mechanism for this Al₃AuIr compound. The present report follows the exploration of the Al–Au–Ir system and introduces the new Al₉(Au;Ir)₄ compound. The crystal structure of this new ternary phase has been determined with single-crystal X-ray diffraction and will be presented and discussed.

2. Experimental details

A sample weighing 0.3 g with a nominal composition of Al₆₉Au₃Ir₂₈ was first prepared by arc melting under 50 kPa of argon from materials of high purity. The sample was inverted and remelted several times to ensure homogeneity. A mass loss of about 2% occurred due to the known evaporation of Al during the synthesis. The resulting ingot was deposited in a capped alumina crucible, sealed in an evacuated quartz tube filled with 70 KPa of an He 90%/H₂ 10% gas and annealed at 1173 K for 336 h. Characterization of the phases has been carried out using powder X-ray diffraction (PXRD) on a D8 Advance Bruker diffractometer using Cu Kα₁ radiation (λ = 1.54056 Å). Single-crystal X-ray diffraction (SC-XRD) data were collected on a Bruker Kappa APEX-II diffractometer equipped with a mirror monochromator and a Mo Kα microfocus source (IμS, λ = 0.71073 Å). The APEX2 program package (Bruker, 2004 ) was used for the cell refinements and data reductions. The crystal structure was solved using direct methods and refined with the SHELXL-2013 program (Sheldrick, 2008 ). Semi-empirical absorption correction (SADABS; Krause et al., 2015 ) was applied to the data. The sample was also mechanically polished to a maximum grain size of 0.25 µm and micrographs were obtained with scanning electron microscopy (SEM) in a Philips XL30S-FEG. Local chemical compositions were obtained in SEM with energy-dispersive X-ray spectroscopy (EDS) and with wavelength-dispersive X-ray spectroscopy (WDS) on a Jeol 8530-F electron microprobe.

3. Results and discussion

3.1. General observations

The PXRD pattern of the sample after the heat treatment is presented in Fig. 1. This pattern can be partially indexed with diffraction peaks from the two known AlIr and Al₃AuIr compounds. The remaining reflections cannot be attributed to any other known Al–Ir or Al–Au binary compound, hence suggesting the stabilization of a new ternary phase. The presence of three phases could be confirmed with SEM analysis. Fig. 2 shows a SEM micrograph of a section of the sample taken in back-scattered electron (BSE) mode. Two phases in two different shades of grey can be identified on this picture. Black areas are pores in the sample.

Figure 1
PXRD pattern of the annealed sample obtained with Cu Kα₁ radiation (λ = 1.54056 Å). Aside from the known AlIr and Al₃AuIr phases, the remaining peaks correspond to the new ternary compound.

Figure 2
A scanning electron micrograph of the polished sample obtained in BSE mode. The light grey phase corresponds to Al₃AuIr and the dark grey one to the new ternary compound. Black areas are pores.

From EDS analysis, the light grey and dark grey phases correspond, respectively, to the Al₃AuIr compound and to a ternary Al–Au–Ir composition with a low gold content. As determined by SEM analysis, the latter is the dominant phase in agreement with the relatively intense unknown diffraction peaks found in the PXRD patterns. The presence of the AlIr compound could also be confirmed in another area of the sample. WDS has been carried out in several regions of the sample containing the new ternary phase in order to obtain a precise chemical composition. The measurements (200 points) lead to an average composition of Al_68.5(2)Au_2.4(2)Ir_29.1(2).

3.2. Crystal structure analysis

A single crystal suitable for data collection was obtained by crushing the sample that provided the material for SEM analysis. Evaluation of the data set reveals a tetragonal unit cell with parameters a = 8.6339 and c = 21.8874 (7) Å. Because of the very similar scattering factors of Au and Ir, these atoms could not be differentiated when solving SC-XRD data and thus were considered only as Ir atoms. The crystal structure was successfully solved by direct methods in the tetragonal space group I4₁/acd with 104 atoms in the unit cell. The reliability factors of this structure model are R₁(all) = 2.5% and wR₂(all) = 4.32%. From the chemical composition of Al_68.5Au_2.4Ir_29.1 given by WDS and considering the 104 atoms per unit cell given by the structure model, an average of 2.5 Au atoms is expected within the unit cell of this compound. This is consistent with a statistical distribution of the Au atoms on the Ir atomic positions, a feature expected for transition metals (TM) having a difference of only two electrons. A similar case of statistical distribution of Au/Ir atoms on the same atomic position was found in the Al₃AuIr crystal structure (Kadok et al., 2015). Thus, the crystal structure of the new ternary phase has been refined considering that the TM sites were occupied with a mixed Au/Ir content. The occupancy ratio has been fixed to the value given by the WDS composition, i.e. considering 2.5 Au atoms among the 104 atoms of the unit cell which leads to a Au/Ir occupancy ratio of 0.08/0.92. Reliability factors did not significantly change after this refinement compared with the model considering only Al and Ir atoms. As given in the crystallographic data information in Table 1, the final chemical formula for this new compound is Al₉Au_xIr_4−x, x = $[{{5} \over {16}}]$ . Considering the mixed Au/Ir occupancy at certain atomic positions, the composition of this new compound is referred to as Al₉(Au;Ir)₄. However, during the exploration of the Al–Au–Ir system, this new compound could not be found with a gold content much higher than 2.5%, hence suggesting a narrow homogeneity range.

Table 1
Experimental details for Al₉(Au;Ir)₄

Crystal data
Chemical formula	Al₇₂Au_2.5Ir_29.5
M_r	8104.88
Crystal system, space group	Tetragonal I4₁/acd
Temperature (K)	296
a, c (Å)	8.6339 (2), 21.8874 (7)
V (Å³)	1631.58 (9)
Z	1
Radiation type	Mo Kα
μ (mm⁻¹)	66.45
Crystal size (mm)	0.05 × 0.05 × 0.01

Data collection
Diffractometer	Bruker APEX-II QUAZAR CCD
Absorption correction	Multi-scan†
T_min, T_max	0.274, 0.749
No. of measured, independent and observed [I > 2σ(I)] reflections	44 132, 1629, 1177
R_int	0.064
(sin θ/λ)_max (Å⁻¹)	0.983

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.017, 0.043, 1.13
No. of reflections	1629
No. of parameters	35
	w = 1/[σ²(F_o²) + (0.0139P)² + 16.567P] where P = (F_o² + 2F_c²)/3
Δρ_max, Δρ_min (e Å⁻³)	4.05, −1.85

†SADABS 2014/5 (Krause et al., 2015

The atomic positions and isotropic displacement parameters are listed in Table 2 and anisotropic displacement parameters in Table 3. In the structure of Al₉(Au;Ir)₄, the heavy atoms of Au and Ir are distributed in two 16-fold atomic positions. These two positions are each coordinated with a 9-Al polyhedron, both constituted of four Al1, four Al2 and one Al3 atoms. They can both be described by comparable capped quadratic prisms, one being slightly distorted compared with the other one. A representation of these atomic environments is depicted in Fig. 3 and a whole unit cell is shown in Fig. 4.

Table 2
Fractional atomic coordinates and equivalent isotropic displacement parameters for Al₉(Au;Ir)₄

Atom	Site	x	y	z	U_eq (Å²)	Occupancy
Au1/Ir1	16d	0	$[{\textstyle{{1} \over {4}}}]$	0.01467 (2)	0.00316 (4)	0.08/0.92
Au2/Ir2	16f	0.19858 (2)	0.44858 (2)	$[{\textstyle{{1} \over {8}}}]$	0.00368 (3)	0.08/0.92
Al1	32g	0.04687 (12)	0.03071 (12)	0.31109 (4)	0.0063 (2)	1
Al2	32g	0.27779 (12)	0.19958 (12)	0.19068 (5)	0.0068 (2)	1
Al3	8b	0	$[{{1}\over{4}}]$	$[{{1}\over{8}}]$	0.0060 (3)	1

Table 3
Anisotropic atomic displacement parameters (Å²) for Al₉(Au;Ir)₄

Atom	U₁₁	U₂₂	U₃₃	U₁₂	U₁₃	U₂₃
Au1/Ir1	0.00365 (14)	0.00361 (13)	0.00224 (5)	0.00039 (3)	0	0
Au2/Ir2	0.00358 (4)	U₁₁	0.00390 (5)	0.00009 (3)	0	0
Al1	0.0084 (4)	0.0049 (4)	0.0057 (4)	0.0003 (3)	0.0004 (3)	0.0012 (3)
Al2	0.0049 (4)	0.0091 (4)	0.0064 (4)	0.0003 (3)	−0.0010 (3)	−0.0015 (3)
Al3	0.0080 (4)	U₁₁	0.0020 (6)	−0.0043 (5)	0	0

Figure 3
Coordination polyhedra around the Au1/Ir1 (left) and Au2/Ir2 (right) positions, having a twofold symmetry along the c and a axes, respectively.

Figure 4
Distribution of the Al polyhedra built around the Au1/Ir1 (left) and Au2/Ir2 (right) atomic positions in the unit cell of the Al₉(Au;Ir)₄ compound reported here. Au1/Ir1 polyhedra are connected by sharing Al3 positions along the c axis and Al1–Al1 or Al2–Al2 edges in the (ab) plane. Au2/Ir2 polyhedra are only connected in the (ab) plane by sharing Al3 positions or Al1–Al2 edges.

The isomorphic structure is found for the BGa₈Ir₄ compound (Kluenter & Jung, 1995 ). Compared with the Al₉(Au;Ir)₄ compound reported here, the Ir atoms in BGa₈Ir₄ are located at the 16d and 16f atomic positions (here Au1/Ir1 and Au2/Ir2, respectively), the Ga atoms at the two 32g positions (here Al1 and Al2) and the B atoms at the 8b positions (here Al3). As for the Ir—B bonds in BGa₈Ir₄, Au1/Ir1—Al3 and Au2/Ir2—Al3 are the shortest bonds in Al₉(Au;Ir)₄ (see Table 4). The similarity between these two crystal structures is not too surprising since B, Al and Ga belong to the same column of the periodic table. It is known that, within a given ternary system, substituting a TM or a metalloid element by an element of the same column of the periodic table can lead sometimes to an isomorphic structure (Tsai et al., 1988 ).

Table 4
Main interatomic distances for Au1/Ir1 and Au2/Ir2 atoms in Al₉(Au;Ir)₄

Atoms	Distance (Å)
Au1/Ir1—2Al1	2.5491 (10)
Au1/Ir1—2Al1	2.6589 (10)
Au1/Ir1—2Al2	2.5481 (10)
Au1/Ir1—2Al2	2.6262 (10)
Au1/Ir1—1Al3	2.41478 (15)
Au2/Ir2—2Al1	2.6113 (11)
Au2/Ir2—2Al1	2.6364 (10)
Au2/Ir2—2Al2	2.6086 (10)
Au2/Ir2—2Al2	2.6751 (11)
Au2/Ir2—1Al3	2.42465 (14)

The Al₉(Au;Ir)₄ compound reported here has a very low Au content, i.e. close to a binary Al–Ir compound. However, there are no similarities found with other crystal structures present in the Al–Ir system, although atomic positions of TM in Al₉(Au;Ir)₄ are shared by both Au and Ir, having a difference of two electrons. The requirement of partial substitution of Ir by Au to stabilize this new structure may either have an electronic or an entropic origin. A Hume–Rothery-type stabilization mechanism is indeed frequently observed in Al–TM compounds in which a Fermi sphere–Brillouin zone interaction plays a key role to lower the total energy of the system. In this case, the Hume–Rothery condition 2k_F = K_hkl must be satisfied for some strong Bragg planes (Massalski & Mizutani, 1978 ; Trambly de Laissardière et al., 2005 ). The Fermi vector can be estimated within a free electron model approximation and assuming an electron valence of +3 and +1 for Al and Au, respectively. A negative valence of −1.6 is attributed to Ir by Raynor (1949 ) while a more recent approach developed by Mizutani & Sato (2017 ) gives a value of +1.6. It leads to 2k_F = 2.88 Å⁻¹ or 2k_F = 3.35 Å⁻¹, respectively. These values are close to K₀₄₀ (2.91 Å⁻¹) and K₂₂₈ (3.09 Å⁻¹) in the former case and close to K₂₂₄ (3.45 Å⁻¹) in the latter case, all of these Bragg planes producing strong reflections. This suggests that the Hume–Rothery condition may be satisfied. However, the average number of valence electrons per atom is only weakly modified by the Au/Ir substitution (only 2.5 Au atoms per unit cell) and the Fermi wavevector is not significantly affected (it changes by only a few 10⁻² Å⁻¹). Therefore the requirement for partial Ir/Au substitution is probably not of electronic origin but rather entropic.

A comparable situation is found in the Al–Si–Ir system. Ongoing work is revealing the existence of a new ternary compound where Si atoms are statistically distributed among the Al atomic positions (Kadok et al., 2019 ). The latter also has a low content of Si, an element which has one electron more than Al. Further details concerning the stability of such a compound will be given in an upcoming report.

4. Conclusion

Al₉(Au;Ir)₄ is the latest ternary compound reported for the Al–Au–Ir system. Just as for Al₃AuIr, the atomic structure shows a statistical distribution of the Au and Ir atoms on the same atomic positions. This phenomenon is likely to arise from the close chemistry between these two elements which differ by only two in the number of electrons they possess. With 104 atoms in a tetragonal crystal system, the Al₉(Au;Ir)₄ compound is isostructural to BGa₈Ir₄, with well-defined atomic clusters of Al surrounding TM atoms. The exploration of the Al-rich side of the Al–Au–Ir system will be pursued to unveil possible additional ternary compounds.

Supporting information

CCDC reference: 1881225

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2052520618016712/dq5033sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2052520618016712/dq5033Isup2.hkl

Computing details top

Data collection: APEX2 (Bruker, 2004); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT; program(s) used to solve structure: SHELXL2014 (Sheldrick, 2014); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2014).

(I) top

Crystal data top

Al₇₂Au_2.50Ir_29.50	D_x = 8.249 Mg m⁻³
M_r = 8104.88	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, I4₁/acd	Cell parameters from 9909 reflections
a = 8.6339 (2) Å	θ = 3.7–44.3°
c = 21.8874 (7) Å	µ = 66.45 mm⁻¹
V = 1631.58 (9) Å³	T = 296 K
Z = 1	Platelet, black
F(000) = 3405	0.05 × 0.05 × 0.01 mm

Data collection top

Bruker APEX-II QUAZAR CCD diffractometer	1177 reflections with I > 2σ(I)
Radiation source: micro sources	R_int = 0.064
ω scan	θ_max = 44.3°, θ_min = 3.8°
Absorption correction: multi-scan SADABS 2014/5	h = −16→16
T_min = 0.274, T_max = 0.749	k = −16→16
44132 measured reflections	l = −42→42
1629 independent reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.0139P)² + 16.567P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.017	(Δ/σ)_max = 0.002
wR(F²) = 0.043	Δρ_max = 4.05 e Å⁻³
S = 1.13	Δρ_min = −1.85 e Å⁻³
1629 reflections	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
35 parameters	Extinction coefficient: 0.000130 (10)

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Ir1	0.0000	0.2500	0.01467 (2)	0.00316 (4)	0.923 (4)
Au1	0.0000	0.2500	0.01467 (2)	0.00316 (4)	0.0782 (4)
Ir2	0.19858 (2)	0.44858 (2)	0.1250	0.00368 (3)	0.922 (4)
Au2	0.19858 (2)	0.44858 (2)	0.1250	0.00368 (3)	0.0781 (3)
Al1	0.04687 (12)	0.03071 (12)	0.31109 (4)	0.0063 (2)
Al2	0.27779 (12)	0.19958 (12)	0.19068 (5)	0.0068 (2)
Al3	0.0000	0.2500	0.1250	0.0060 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ir1	0.00365 (14)	0.00361 (13)	0.00224 (5)	0.00039 (3)	0.000	0.000
Au1	0.00365 (14)	0.00361 (13)	0.00224 (5)	0.00039 (3)	0.000	0.000
Ir2	0.00358 (4)	0.00358 (4)	0.00390 (5)	0.00009 (3)	0.00000 (3)	0.00000 (3)
Au2	0.00358 (4)	0.00358 (4)	0.00390 (5)	0.00009 (3)	0.00000 (3)	0.00000 (3)
Al1	0.0084 (4)	0.0049 (4)	0.0057 (4)	0.0003 (3)	0.0004 (3)	0.0012 (3)
Al2	0.0049 (4)	0.0091 (4)	0.0064 (4)	0.0003 (3)	−0.0010 (3)	−0.0015 (3)
Al3	0.0080 (4)	0.0080 (4)	0.0020 (6)	−0.0043 (5)	0.000	0.000

Geometric parameters (Å, º) top

Ir1—Al3	2.4148 (1)	Al1—Ir1^xi	2.6589 (10)
Ir1—Al2ⁱ	2.5481 (10)	Al1—Au1^xi	2.6589 (10)
Ir1—Al2ⁱⁱ	2.5481 (10)	Al1—Al1^xii	2.726 (2)
Ir1—Al1ⁱⁱⁱ	2.5491 (10)	Al1—Al2^xiii	2.7431 (15)
Ir1—Al1^iv	2.5491 (10)	Al1—Al2^ix	2.7778 (15)
Ir1—Al2ⁱⁱⁱ	2.6262 (10)	Al1—Al2^xii	2.8160 (14)
Ir1—Al2^iv	2.6262 (10)	Al2—Au1^xiv	2.5481 (10)
Ir1—Al1^v	2.6589 (10)	Al2—Ir1^xiv	2.5481 (10)
Ir1—Al1^vi	2.6589 (10)	Al2—Au2^xv	2.6086 (10)
Ir2—Al3	2.4247 (1)	Al2—Ir2^xv	2.6086 (10)
Ir2—Al2^vii	2.6086 (10)	Al2—Ir1ⁱⁱⁱ	2.6262 (10)
Ir2—Al2^viii	2.6086 (10)	Al2—Au1ⁱⁱⁱ	2.6262 (10)
Ir2—Al1^ix	2.6113 (11)	Al2—Al1^xvi	2.7431 (15)
Ir2—Al1ⁱⁱ	2.6113 (11)	Al2—Al1^ix	2.7778 (15)
Ir2—Al1^v	2.6364 (10)	Al2—Al2^ix	2.780 (2)
Ir2—Al1^x	2.6364 (10)	Al2—Al1^xii	2.8160 (14)
Ir2—Al2ⁱⁱⁱ	2.6751 (11)	Al3—Au1ⁱⁱⁱ	2.4148 (1)
Ir2—Al2	2.6751 (11)	Al3—Ir1ⁱⁱⁱ	2.4148 (1)
Al1—Au1ⁱⁱⁱ	2.5492 (10)	Al3—Au2^xvii	2.4247 (1)
Al1—Ir1ⁱⁱⁱ	2.5492 (10)	Al3—Ir2^xvii	2.4247 (1)
Al1—Au2^ix	2.6113 (11)	Al3—Al1^x	2.8274 (10)
Al1—Ir2^ix	2.6113 (11)	Al3—Al1^vi	2.8274 (10)
Al1—Au2^xi	2.6363 (10)	Al3—Al1^v	2.8274 (10)
Al1—Ir2^xi	2.6363 (10)	Al3—Al1^xii	2.8274 (10)

Al3—Ir1—Al2ⁱ	129.46 (2)	Au2^ix—Al1—Al2^ix	59.43 (3)
Al3—Ir1—Al2ⁱⁱ	129.46 (2)	Ir2^ix—Al1—Al2^ix	59.43 (3)
Al2ⁱ—Ir1—Al2ⁱⁱ	101.08 (5)	Au2^xi—Al1—Al2^ix	132.14 (5)
Al3—Ir1—Al1ⁱⁱⁱ	130.58 (2)	Ir2^xi—Al1—Al2^ix	132.14 (5)
Al2ⁱ—Ir1—Al1ⁱⁱⁱ	65.12 (4)	Ir1^xi—Al1—Al2^ix	147.32 (4)
Al2ⁱⁱ—Ir1—Al1ⁱⁱⁱ	66.04 (4)	Au1^xi—Al1—Al2^ix	147.32 (4)
Al3—Ir1—Al1^iv	130.58 (2)	Al1^xii—Al1—Al2^ix	98.59 (5)
Al2ⁱ—Ir1—Al1^iv	66.04 (4)	Al2^xiii—Al1—Al2^ix	90.90 (4)
Al2ⁱⁱ—Ir1—Al1^iv	65.12 (4)	Au1ⁱⁱⁱ—Al1—Al2^xii	128.89 (5)
Al1ⁱⁱⁱ—Ir1—Al1^iv	98.84 (5)	Ir1ⁱⁱⁱ—Al1—Al2^xii	128.89 (5)
Al3—Ir1—Al2ⁱⁱⁱ	68.16 (2)	Au2^ix—Al1—Al2^xii	57.31 (3)
Al2ⁱ—Ir1—Al2ⁱⁱⁱ	153.61 (4)	Ir2^ix—Al1—Al2^xii	57.31 (3)
Al2ⁱⁱ—Ir1—Al2ⁱⁱⁱ	64.99 (4)	Au2^xi—Al1—Al2^xii	112.74 (4)
Al1ⁱⁱⁱ—Ir1—Al2ⁱⁱⁱ	88.51 (3)	Ir2^xi—Al1—Al2^xii	112.74 (4)
Al1^iv—Ir1—Al2ⁱⁱⁱ	120.67 (3)	Ir1^xi—Al1—Al2^xii	57.24 (3)
Al3—Ir1—Al2^iv	68.16 (2)	Au1^xi—Al1—Al2^xii	57.24 (3)
Al2ⁱ—Ir1—Al2^iv	64.99 (4)	Al1^xii—Al1—Al2^xii	81.32 (4)
Al2ⁱⁱ—Ir1—Al2^iv	153.61 (4)	Al2^xiii—Al1—Al2^xii	167.09 (5)
Al1ⁱⁱⁱ—Ir1—Al2^iv	120.67 (3)	Al2^ix—Al1—Al2^xii	101.88 (3)
Al1^iv—Ir1—Al2^iv	88.51 (3)	Au1^xiv—Al2—Ir1^xiv	0.000 (4)
Al2ⁱⁱⁱ—Ir1—Al2^iv	136.31 (4)	Au1^xiv—Al2—Au2^xv	115.68 (4)
Al3—Ir1—Al1^v	67.54 (2)	Ir1^xiv—Al2—Au2^xv	115.68 (4)
Al2ⁱ—Ir1—Al1^v	106.50 (4)	Au1^xiv—Al2—Ir2^xv	115.68 (4)
Al2ⁱⁱ—Ir1—Al1^v	101.64 (3)	Ir1^xiv—Al2—Ir2^xv	115.68 (4)
Al1ⁱⁱⁱ—Ir1—Al1^v	161.75 (2)	Au2^xv—Al2—Ir2^xv	0.000 (2)
Al1^iv—Ir1—Al1^v	63.09 (4)	Au1^xiv—Al2—Ir1ⁱⁱⁱ	115.01 (4)
Al2ⁱⁱⁱ—Ir1—Al1^v	98.51 (3)	Ir1^xiv—Al2—Ir1ⁱⁱⁱ	115.01 (4)
Al2^iv—Ir1—Al1^v	64.39 (3)	Au2^xv—Al2—Ir1ⁱⁱⁱ	114.47 (4)
Al3—Ir1—Al1^vi	67.54 (2)	Ir2^xv—Al2—Ir1ⁱⁱⁱ	114.47 (4)
Al2ⁱ—Ir1—Al1^vi	101.64 (3)	Au1^xiv—Al2—Au1ⁱⁱⁱ	115.01 (4)
Al2ⁱⁱ—Ir1—Al1^vi	106.50 (4)	Ir1^xiv—Al2—Au1ⁱⁱⁱ	115.01 (4)
Al1ⁱⁱⁱ—Ir1—Al1^vi	63.09 (4)	Au2^xv—Al2—Au1ⁱⁱⁱ	114.47 (4)
Al1^iv—Ir1—Al1^vi	161.75 (2)	Ir2^xv—Al2—Au1ⁱⁱⁱ	114.47 (4)
Al2ⁱⁱⁱ—Ir1—Al1^vi	64.39 (3)	Ir1ⁱⁱⁱ—Al2—Au1ⁱⁱⁱ	0.000 (5)
Al2^iv—Ir1—Al1^vi	98.51 (3)	Au1^xiv—Al2—Ir2	113.37 (4)
Al1^v—Ir1—Al1^vi	135.07 (4)	Ir1^xiv—Al2—Ir2	113.37 (4)
Al3—Ir2—Al2^vii	130.00 (2)	Au2^xv—Al2—Ir2	113.04 (4)
Al3—Ir2—Al2^viii	130.00 (2)	Ir2^xv—Al2—Ir2	113.04 (4)
Al2^vii—Ir2—Al2^viii	100.01 (5)	Ir1ⁱⁱⁱ—Al2—Ir2	80.40 (3)
Al3—Ir2—Al1^ix	130.06 (2)	Au1ⁱⁱⁱ—Al2—Ir2	80.40 (3)
Al2^vii—Ir2—Al1^ix	65.29 (3)	Au1^xiv—Al2—Al1^xvi	57.46 (3)
Al2^viii—Ir2—Al1^ix	65.84 (3)	Ir1^xiv—Al2—Al1^xvi	57.46 (3)
Al3—Ir2—Al1ⁱⁱ	130.06 (2)	Au2^xv—Al2—Al1^xvi	58.96 (3)
Al2^vii—Ir2—Al1ⁱⁱ	65.84 (3)	Ir2^xv—Al2—Al1^xvi	58.96 (3)
Al2^viii—Ir2—Al1ⁱⁱ	65.29 (3)	Ir1ⁱⁱⁱ—Al2—Al1^xvi	150.09 (5)
Al1^ix—Ir2—Al1ⁱⁱ	99.88 (4)	Au1ⁱⁱⁱ—Al2—Al1^xvi	150.09 (5)
Al3—Ir2—Al1^v	67.78 (2)	Ir2—Al2—Al1^xvi	129.50 (5)
Al2^vii—Ir2—Al1^v	159.91 (3)	Au1^xiv—Al2—Al1^ix	57.00 (3)
Al2^viii—Ir2—Al1^v	63.06 (3)	Ir1^xiv—Al2—Al1^ix	57.00 (3)
Al1^ix—Ir2—Al1^v	96.48 (4)	Au2^xv—Al2—Al1^ix	130.25 (4)
Al1ⁱⁱ—Ir2—Al1^v	111.95 (3)	Ir2^xv—Al2—Al1^ix	130.25 (4)
Al3—Ir2—Al1^x	67.78 (2)	Ir1ⁱⁱⁱ—Al2—Al1^ix	111.34 (4)
Al2^vii—Ir2—Al1^x	63.06 (3)	Au1ⁱⁱⁱ—Al2—Al1^ix	111.34 (4)
Al2^viii—Ir2—Al1^x	159.91 (3)	Ir2—Al2—Al1^ix	57.19 (3)
Al1^ix—Ir2—Al1^x	111.95 (3)	Al1^xvi—Al2—Al1^ix	89.07 (4)
Al1ⁱⁱ—Ir2—Al1^x	96.48 (4)	Au1^xiv—Al2—Al2^ix	58.86 (4)
Al1^v—Ir2—Al1^x	135.56 (4)	Ir1^xiv—Al2—Al2^ix	58.86 (4)
Al3—Ir2—Al2ⁱⁱⁱ	67.20 (2)	Au2^xv—Al2—Al2^ix	142.03 (6)
Al2^vii—Ir2—Al2ⁱⁱⁱ	98.43 (4)	Ir2^xv—Al2—Al2^ix	142.03 (6)
Al2^viii—Ir2—Al2ⁱⁱⁱ	110.58 (3)	Ir1ⁱⁱⁱ—Al2—Al2^ix	56.15 (4)
Al1^ix—Ir2—Al2ⁱⁱⁱ	161.22 (3)	Au1ⁱⁱⁱ—Al2—Al2^ix	56.15 (4)
Al1ⁱⁱ—Ir2—Al2ⁱⁱⁱ	63.38 (3)	Ir2—Al2—Al2^ix	101.89 (5)
Al1^v—Ir2—Al2ⁱⁱⁱ	97.85 (3)	Al1^xvi—Al2—Al2^ix	109.01 (6)
Al1^x—Ir2—Al2ⁱⁱⁱ	64.56 (3)	Al1^ix—Al2—Al2^ix	81.06 (5)
Al3—Ir2—Al2	67.20 (2)	Au1^xiv—Al2—Al1^xii	131.49 (5)
Al2^vii—Ir2—Al2	110.58 (3)	Ir1^xiv—Al2—Al1^xii	131.49 (5)
Al2^viii—Ir2—Al2	98.43 (4)	Au2^xv—Al2—Al1^xii	57.40 (3)
Al1^ix—Ir2—Al2	63.38 (3)	Ir2^xv—Al2—Al1^xii	57.40 (3)
Al1ⁱⁱ—Ir2—Al2	161.22 (3)	Ir1ⁱⁱⁱ—Al2—Al1^xii	58.37 (3)
Al1^v—Ir2—Al2	64.56 (3)	Au1ⁱⁱⁱ—Al2—Al1^xii	58.37 (3)
Al1^x—Ir2—Al2	97.85 (3)	Ir2—Al2—Al1^xii	112.27 (4)
Al2ⁱⁱⁱ—Ir2—Al2	134.40 (4)	Al1^xvi—Al2—Al1^xii	102.95 (4)
Au1ⁱⁱⁱ—Al1—Ir1ⁱⁱⁱ	0.000 (4)	Al1^ix—Al2—Al1^xii	167.85 (5)
Au1ⁱⁱⁱ—Al1—Au2^ix	115.54 (4)	Al2^ix—Al2—Al1^xii	96.42 (5)
Ir1ⁱⁱⁱ—Al1—Au2^ix	115.54 (4)	Ir1—Al3—Au1ⁱⁱⁱ	180.0
Au1ⁱⁱⁱ—Al1—Ir2^ix	115.54 (4)	Ir1—Al3—Ir1ⁱⁱⁱ	180.0
Ir1ⁱⁱⁱ—Al1—Ir2^ix	115.54 (4)	Au1ⁱⁱⁱ—Al3—Ir1ⁱⁱⁱ	0.0
Au2^ix—Al1—Ir2^ix	0.000 (6)	Ir1—Al3—Ir2	90.0
Au1ⁱⁱⁱ—Al1—Au2^xi	114.67 (4)	Au1ⁱⁱⁱ—Al3—Ir2	90.0
Ir1ⁱⁱⁱ—Al1—Au2^xi	114.67 (4)	Ir1ⁱⁱⁱ—Al3—Ir2	90.0
Au2^ix—Al1—Au2^xi	114.25 (4)	Ir1—Al3—Au2^xvii	90.0
Ir2^ix—Al1—Au2^xi	114.25 (4)	Au1ⁱⁱⁱ—Al3—Au2^xvii	90.0
Au1ⁱⁱⁱ—Al1—Ir2^xi	114.67 (4)	Ir1ⁱⁱⁱ—Al3—Au2^xvii	90.0
Ir1ⁱⁱⁱ—Al1—Ir2^xi	114.67 (4)	Ir2—Al3—Au2^xvii	180.0
Au2^ix—Al1—Ir2^xi	114.25 (4)	Ir1—Al3—Ir2^xvii	90.0
Ir2^ix—Al1—Ir2^xi	114.25 (4)	Au1ⁱⁱⁱ—Al3—Ir2^xvii	90.0
Au2^xi—Al1—Ir2^xi	0.000 (1)	Ir1ⁱⁱⁱ—Al3—Ir2^xvii	90.0
Au1ⁱⁱⁱ—Al1—Ir1^xi	113.85 (4)	Ir2—Al3—Ir2^xvii	180.0
Ir1ⁱⁱⁱ—Al1—Ir1^xi	113.85 (4)	Au2^xvii—Al3—Ir2^xvii	0.000 (6)
Au2^ix—Al1—Ir1^xi	113.28 (4)	Ir1—Al3—Al1^x	119.65 (2)
Ir2^ix—Al1—Ir1^xi	113.28 (4)	Au1ⁱⁱⁱ—Al3—Al1^x	60.35 (2)
Au2^xi—Al1—Ir1^xi	80.52 (3)	Ir1ⁱⁱⁱ—Al3—Al1^x	60.35 (2)
Ir2^xi—Al1—Ir1^xi	80.52 (3)	Ir2—Al3—Al1^x	59.67 (2)
Au1ⁱⁱⁱ—Al1—Au1^xi	113.85 (4)	Au2^xvii—Al3—Al1^x	120.33 (2)
Ir1ⁱⁱⁱ—Al1—Au1^xi	113.85 (4)	Ir2^xvii—Al3—Al1^x	120.33 (2)
Au2^ix—Al1—Au1^xi	113.28 (4)	Ir1—Al3—Al1^vi	60.35 (2)
Ir2^ix—Al1—Au1^xi	113.28 (4)	Au1ⁱⁱⁱ—Al3—Al1^vi	119.65 (2)
Au2^xi—Al1—Au1^xi	80.52 (3)	Ir1ⁱⁱⁱ—Al3—Al1^vi	119.65 (2)
Ir2^xi—Al1—Au1^xi	80.52 (3)	Ir2—Al3—Al1^vi	120.33 (2)
Ir1^xi—Al1—Au1^xi	0.000 (5)	Au2^xvii—Al3—Al1^vi	59.67 (2)
Au1ⁱⁱⁱ—Al1—Al1^xii	60.42 (4)	Ir2^xvii—Al3—Al1^vi	59.67 (2)
Ir1ⁱⁱⁱ—Al1—Al1^xii	60.42 (4)	Al1^x—Al3—Al1^vi	89.97 (4)
Au2^ix—Al1—Al1^xii	122.60 (2)	Ir1—Al3—Al1^v	60.35 (2)
Ir2^ix—Al1—Al1^xii	122.60 (2)	Au1ⁱⁱⁱ—Al3—Al1^v	119.65 (2)
Au2^xi—Al1—Al1^xii	117.91 (3)	Ir1ⁱⁱⁱ—Al3—Al1^v	119.65 (2)
Ir2^xi—Al1—Al1^xii	117.91 (3)	Ir2—Al3—Al1^v	59.67 (2)
Ir1^xi—Al1—Al1^xii	56.49 (4)	Au2^xvii—Al3—Al1^v	120.33 (2)
Au1^xi—Al1—Al1^xii	56.49 (4)	Ir2^xvii—Al3—Al1^v	120.33 (2)
Au1ⁱⁱⁱ—Al1—Al2^xiii	57.42 (3)	Al1^x—Al3—Al1^v	119.35 (4)
Ir1ⁱⁱⁱ—Al1—Al2^xiii	57.42 (3)	Al1^vi—Al3—Al1^v	120.69 (4)
Au2^ix—Al1—Al2^xiii	133.16 (5)	Ir1—Al3—Al1^xii	119.65 (2)
Ir2^ix—Al1—Al2^xiii	133.16 (5)	Au1ⁱⁱⁱ—Al3—Al1^xii	60.35 (2)
Au2^xi—Al1—Al2^xiii	57.97 (3)	Ir1ⁱⁱⁱ—Al3—Al1^xii	60.35 (2)
Ir2^xi—Al1—Al2^xiii	57.97 (3)	Ir2—Al3—Al1^xii	120.33 (2)
Ir1^xi—Al1—Al2^xiii	110.50 (4)	Au2^xvii—Al3—Al1^xii	59.67 (2)
Au1^xi—Al1—Al2^xiii	110.50 (4)	Ir2^xvii—Al3—Al1^xii	59.67 (2)
Al1^xii—Al1—Al2^xiii	95.13 (4)	Al1^x—Al3—Al1^xii	120.69 (4)
Au1ⁱⁱⁱ—Al1—Al2^ix	56.96 (3)	Al1^vi—Al3—Al1^xii	119.35 (4)
Ir1ⁱⁱⁱ—Al1—Al2^ix	56.96 (3)	Al1^v—Al3—Al1^xii	89.97 (4)

Symmetry codes: (i) y−1/4, x−1/4, z−1/4; (ii) −y+1/4, −x+3/4, z−1/4; (iii) y−1/4, x+1/4, −z+1/4; (iv) −y+1/4, −x+1/4, −z+1/4; (v) y+1/4, −x+1/4, z−1/4; (vi) −y−1/4, x+1/4, z−1/4; (vii) −x+1/2, y+1/2, z; (viii) y+1/4, −x+3/4, −z+1/4; (ix) −x+1/2, −y+1/2, −z+1/2; (x) −x, y+1/2, −z+1/2; (xi) −y+1/4, x−1/4, z+1/4; (xii) x, −y, −z+1/2; (xiii) x−1/2, y, −z+1/2; (xiv) −y+3/4, −x+1/4, z+1/4; (xv) −y+3/4, x−1/4, −z+1/4; (xvi) x+1/2, y, −z+1/2; (xvii) −x, −y+1/2, z.

Acknowledgements

Christine Gendarme from the CC3M of the IJL is acknowledged for the WDS measurements.

Funding information

Funding for this research was provided by: Centre National de la Recherche Scientifique; Conseil Régional de Lorraine.

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Volume 75| Part 1| February 2019| Pages 49-52

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